Rewrite as a simplified fraction. ${0.8\overline{69} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 869.6969...\\ 10x &= 8.6969...\end{align*}}$ Subtracting the two equations, we have: ${990x = 861}$ ${x = \dfrac{861}{990}} $ ${x = \dfrac{287}{330}} $